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Radar is a critical perception modality in autonomous driving systems due to its all-weather characteristics and ability to measure range and Doppler velocity. However, the sheer volume of high-dimensional raw radar data saturates the…
We consider a compressed sensing problem in which both the measurement and the sparsifying systems are assumed to be frames (not necessarily tight) of the underlying Hilbert space of signals, which may be finite or infinite dimensional. The…
Inverse problems constrained by partial differential equations are often ill-conditioned due to noisy and incomplete data or inherent non-uniqueness. A prominent example is full waveform inversion, which estimates Earth's subsurface…
Integrated sensing and communication improves the design of systems by combining sensing and communication functions for increased efficiency, accuracy, and cost savings. The optimal integration requires understanding the trade-off between…
A derivation of the properties of pulsed radiative imaging systems is presented with examples drawn from conventional, synthetic aperture, and interferometric radar. A geometric construction of the space and time components of a radar…
Recently, the progress in the radar sensing technology consisting in the miniaturization of the packages and increase in measuring precision has drawn the interest of the robotics research community. Indeed, a crucial task enabling autonomy…
Compressed sensing (CS) model of complex-valued data can represent the signal recovery process of a large amount types of radar systems, especially when the measurement matrix is row-orthogonal. Based on debiased least absolute shrinkage…
Consider a target being tracked by a cognitive radar network. If the target can intercept noisy radar emissions, how can it detect coordination in the radar network? By 'coordination' we mean that the radar emissions satisfy Pareto…
Compressed sensing is a novel research area, which was introduced in 2006, and since then has already become a key concept in various areas of applied mathematics, computer science, and electrical engineering. It surprisingly predicts that…
We investigate an empirical Bayesian nonparametric approach to a family of linear inverse problems with Gaussian prior and Gaussian noise. We consider a class of Gaussian prior probability measures with covariance operator indexed by a…
Making good predictions of a physical system using a computer code requires the inputs to be carefully specified. Some of these inputs called control variables have to reproduce physical conditions whereas other inputs, called parameters,…
A trapping region is a compact set that is forward invariant with respect to the dynamics. Existence of a trapping region certifies boundedness of trajectories, and the size of the set provides an estimate of the ultimate bound. Prior work…
To relieve the interference caused by range-Doppler sidelobes in pulsed radars, we propose a new method to construct Doppler resilient complementary waveforms based on Golay codes. We design both the transmit pulse train and the receive…
Range profiling refers to the measurement of target response along the radar slant range. It plays an important role in automatic target recognition. In this paper, we consider the design of transmit waveform to improve the range profiling…
An accurate delay and Doppler estimation method for a radar system using time and frequency-shifted pulses with pseudo-random numbers is proposed. The ambiguity function of the transmitted signal has a strong peak at the origin and is close…
Sparsity is a ubiquitous feature of many real world signals such as natural images and neural spiking activities. Conventional compressed sensing utilizes sparsity to recover low dimensional signal structures in high ambient dimensions…
We propose an innovative meteorological radar, which uses reduced number of spatiotemporal samples without compromising the accuracy of target information. Our approach extends recent research on compressed sensing (CS) for radar remote…
We study full Bayesian procedures for high-dimensional linear regression under sparsity constraints. The prior is a mixture of point masses at zero and continuous distributions. Under compatibility conditions on the design matrix, the…
Statistical procedures rarely retain all features of the observed data. A sufficient statistic removes information irrelevant to a parameter; a maximum likelihood estimate compresses an empirical objective into an optimizing point; and a…
Optimal design of experiments for Bayesian inverse problems has recently gained wide popularity and attracted much attention, especially in the computational science and Bayesian inversion communities. An optimal design maximizes a…